Block #333,004

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/28/2013, 11:28:58 AM · Difficulty 10.1659 · 6,493,140 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

4e5fc5d09ed2c3f9caaea968aa07f8d498f444da61087281127324efd7f3558f

View on Chainz ↗

Height

#333,004

Difficulty

10.165929

Transactions

Size

207 B

Version

Bits

0a2a7a54

Nonce

865,326

Timestamp

12/28/2013, 11:28:58 AM

Confirmations

6,493,140

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5991e2cdd4e1fd8aad0f2eee834cafc4393fa745a6ea61b51a88025eaaab4978

Transactions (1)

Coinbase5991e2cdd4e1fd…88025eaaab4978

1 in → 1 out9.6600 XPM116 B

AbwWkWZt…kawDhufa

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.882 × 10⁹⁸(99-digit number)

18822774683748387914…91454408172365216319

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.882 × 10⁹⁸(99-digit number)

18822774683748387914…91454408172365216319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.882 × 10⁹⁸(99-digit number)

18822774683748387914…91454408172365216321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.764 × 10⁹⁸(99-digit number)

37645549367496775829…82908816344730432639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.764 × 10⁹⁸(99-digit number)

37645549367496775829…82908816344730432641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

7.529 × 10⁹⁸(99-digit number)

75291098734993551659…65817632689460865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.529 × 10⁹⁸(99-digit number)

75291098734993551659…65817632689460865281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.505 × 10⁹⁹(100-digit number)

15058219746998710331…31635265378921730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.505 × 10⁹⁹(100-digit number)

15058219746998710331…31635265378921730561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.011 × 10⁹⁹(100-digit number)

30116439493997420663…63270530757843461119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.011 × 10⁹⁹(100-digit number)

30116439493997420663…63270530757843461121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #333,004

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